I don't know if TK is able to stop them or not, but it's no secret that TK and LY hate each other. El Al cannot stomach the fact that TK is allowed to fly into Israel, while El Al isn't allowed to fly into Istanbul (which I agree isn't very fair). And TK has 9 daily nonstop flights to TLV so they can fight El Al on almost every route with cheap connection options. They're even adding a tenth daily flight now.
https://en.globes.co.il/en/article-turkish-airlines-adding-tenth-daily-flight-from-tel-aviv-1001245958
I don't believe there is any other carrier that has even half that amount of daily flights into TLV from a single destination.
El Al is pretty verbal about it too, as mentioned in the above article
LY hates (or is jealous of) TK, not sure it goes the other way.
I just did a Google search to find out how come LY doesn't fly to IST, and found out that it's an Israeli security issue
https://www.globes.co.il/news/article.aspx?did=1000521175.
Read the sentence carefully, he's complaining about his inability to compete with TK that runs a huge hub at IST, and is able to be competitive to many destinations for people willing to connect. How does LY's inability to compete with TK on a flight to the US (TK flies to more destinations in NA than LY does) have anything to do with the inability to land in IST? It's mixing up two irrelevant issues, the inability to compete on the TLV-IST route (which is very high traffic, not so much due to point-to-point travel but rather as a connection hub - 85% of traffic is a commonly used figure).
ETA: I just went back and read through the article I just posted until the end, and found the following paragraph which I found laughable:
על-פי המתוכנן, בשלב הבא מתכוונת אל-על להפוך את נתב"ג ל"האב", ולהטיס אליו באמצעות חברת אטלס ג'ט תיירים טורקיים שיגיעו מאיסטנבול לנתב"ג, וימשיכו מכאן בטיסות אל-על ליעדים דוגמת ארה"ב או המזרח הרחוק, שאליהם לא טסה אטלס ג'ט.
Seriously? LY is hoping that TLV should become a hub for Turkish travelers that would flock to Atlas for flights to points served by LY?